8r2-2r-7=6r2

Solution for 8r2-2r-7=6r2 equation:

8r^2-2r-7=6r^2

We move all terms to the left:

8r^2-2r-7-(6r^2)=0

determiningTheFunctionDomain
8r^2-6r^2-2r-7=0

We add all the numbers together, and all the variables

2r^2-2r-7=0

a = 2; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·2·(-7)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{15}}{2*2}=\frac{2-2\sqrt{15}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{15}}{2*2}=\frac{2+2\sqrt{15}}{4}
$